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useful tool to assess the potential contribution
and dynamics of ephemeral gully erosion.
Another physically-based approach that could
be used to predict sediment evacuated by gullies
was developed by Istanbulluoglu
et al
. (2003).
They measured cross-sections at several points
within gullies that had formed during a single
intense rainstorm after a forest fire, in the Idaho
Batholith. Using the planimetric map of the gul-
lies they predicted the eroded volume between
the different cross-sections with standard sedi-
ment transport equations as a function of dimen-
sionless shear stress. The latter variable was
calculated from field topographical data (i.e. run-
off contributing area and local slope) and the
characteristics of the rainfall event (i.e. intensity
and duration). Vanwalleghem
et al
. (2009) further
tested this approach in a wider range of condi-
tions and concluded that good results could be
obtained with one single sediment transport
equation for incision that ranged in size from
small rills (several cm wide) to large gullies (sev-
eral metres wide). One important condition,
however, is that the incisions formed during a
single event with well-known hydrological
conditions.
Gully sidewall failure is known to contribute
significantly to channel widening. Statistical
techniques have been applied to analyse and
model gully sidewall erosion. MartÃnez-
Casasnovas
et al
. (2004) used logistic regression
to model the presence-absence of sidewall fail-
ure. Although their model did not include a
measure of soil loss by sidewall failures, they
successfully predicted wall collapse (overall accu-
racy
the more complex landscape evolution model,
they concluded that slab failures have profound
effects on the tempo of topographic evolution.
Sidorchuk (1999) and others (reviewed by
Vanwalleghem
et al
. 2005c) observed that gully
channel formation is very rapid during the period
of gully initiation, when morphological charac-
teristics of a gully (i.e. length, depth, width, area
and volume) are far from stable. This period typi-
cally takes about 5% of a gully's lifetime. For the
remaining part of a gully's lifetime, its size is
near a stable, maximum value. Sidorchuk (1999)
proposed two gully erosion models correspond-
ing to these two stages of gully development:
(1) a dynamic model predicting rapid changes of
gully morphology during the first short period of
gully development; and (2) a static model to cal-
culate the final morphometric parameters of sta-
ble gullies. The dynamic gully model is based on
the solution of the equations of mass conserva-
tion and gully bed deformation. The static gully
model is based on the assumption of a final mor-
phological equilibrium of a gully. Both model
types were tested using data on gully morphology
and dynamics from Yamal peninsula (Russia) and
New South Wales (Australia) (Sidorchuk &
Grigorév, 1998; Sidorchuk, 1999). These models
have been used at the landscape level to evaluate
the effects of gully development at a larger scale.
Sidorchuk
et al
. (2001, 2003) applied the stable
(or static) gully model to the catchment of the
Mbuluzi river in Swaziland, after having subdi-
vided it into erosion response units (ERU). An
ERU is a 3D terrain unit, where an erosion proc-
ess is scarcely spatially varying with respect to
other ERUs (i.e. variation of process type and
intensity increases while further increasing the
ERU size). The application of the modelling
required the definition of a stable channel width,
which resulted for the Mbuluzi river to be
0.3
87%) as a function of variables related to
topography and soil hydrological conditions.
Istanbulluoglu
et al
. (2005) developed a physi-
cally-based approach for the initiation of slab
failures in gullies. Based on a force balance equa-
tion of an assumed failure geometry, they
implemented their numerical model both in a
simple one-dimensional model and in a more
complex three-dimensional landscape evolution
model (CHILD). They showed that their model
could explain 60% of the variability in observed
bank heights in a study area in Colorado. With
=
b
W
=
where
W
b
is the gully bed width and
A
c
is the contributing area (m
2
).
0.5
c
(iii) Modelling gully headcut retreat
Once initi-
ated, (bank) gullies essentially expand by gully
headcut retreat, and to a lesser extent by gully
wall retreat (e.g. Plate 18 and Plate 19). Whether a
